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Yan, Dong (author), Gugushvili, Shota (author), van der Vaart, A.W. (author)We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function...journal article 2024
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Mulder, W.A. (author)To estimate the depth errors in a subsurface model obtained from the inversion of seismic data, the stationary-phase approximation in a two-dimensional constant-velocity model with a dipped reflector is applied to migration with a time-shift extension. This produces two asymptotic solutions: one is a straight line, and the other is a curve....journal article 2024
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Koers, G.J. (author)Imagine you need to navigate through a completely dark cave. A well-known way of achieving this is echolocation, which works by making sounds and listening to how they are reflected back. The problem of determining the geometric shape of a space from a mixture of reflections of emitted sounds, is an example of an inverse problem. In many fields...doctoral thesis 2023
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Manikandan, Rakshith (author)Fibre-reinforced laminated composites are constructed layer-by-layer, allowing their material properties to be easily tailored relative to their isotropic counterparts (metallic alloys). Moreover, a composite structure with variable stiffness (VS) can be made by spatially tailoring stiffness across a laminate. This permits better load...master thesis 2023
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Suresan, Anjali (author)Atrial Fibrillation (AF) is a cardiac arrhythmia that occurs due to the initiation of electrical impulses in the heart in an uncoordinated manner, giving rise to a disorganized and rapid heartbeat. The progression of AF over time can lead to complications such as stroke and heart failure. Catheter ablation is an established treatment protocol...master thesis 2023
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Westerweel, Lucy (author)This thesis aims at introducing the reader to the mathematical concepts behind the imaging technique X-ray tomography, commonly known as a CT scan. It includes the derivation of the filtered and unfiltered backprojection reconstruction methods for noise-free data. It was concluded that for noisy data, X-ray tomography is an ill-posed, and...bachelor thesis 2023
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Licurici, Teodor (author)Estimating the transmembrane currents travelling through the epicardium and local activation times based on atrial epicardial electrograms can greatly help in the study of cardiac arrhythmias such as atrial fibrillation. This work focuses on the accurate estimation of the aforementioned signals and features. To do this, two least squares-based...master thesis 2023
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Hopman, Luuk (author)Asphalt concrete is one of the most widely used materials in modern road construction. Predicting its functional properties is crucial in the design of new asphalt concrete mixtures. However, current prediction models are limited in accuracy and applicability due to the complex nature of asphalt concrete properties. This thesis researches the...master thesis 2023
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van Zwieten, G.J. (author)A vital component in the management of seismic hazard is the study of past seismic events. Classically, this has been the domain of seismology, which studies the dynamic manifestations of the event to infer properties such as epicenter and moment magnitude. More recently it has become possible to perform similar analyses on the basis of the...doctoral thesis 2023
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Boddapati, Jagannadh (author), Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author), Daraio, Chiara (author)When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic stiffness parameters, as opposed to only 2 needed for isotropic materials. Such high number of parameters...journal article 2023
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Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We extend the scope of our recently developed approach for unsupervised automated discovery of material laws (denoted as EUCLID) to the general case of a material belonging to an unknown class of constitutive behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive...journal article 2023
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Kekkonen, H.N. (author), Lassas, Matti (author), Saksman, Eero (author), Siltanen, Samuli (author)We propose alternatives to Bayesian prior distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-preserving properties as total variation or Mumford-Shah priors but correspond to well-defined infinite-dimensional random variables, and can be approximated by finite...journal article 2023
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Hunter, William (author)Atrial fibrillation is a common cardiovascular disease, affecting the regular beating of the heart through chaotic contraction of the heart's upper chambers. On its own, the condition—increasingly prevalent among the elderly—is not life threatening, but it leads to an increased risk of stroke and heart failure. As of yet, there is no consensus...master thesis 2022
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Ansuinelli, P. (author)The importance of inverse problems is paramount in science and physics because their solution provides information about parameters that cannot be directly observed. This thesis discusses and details the application of a few inverse methods in optical imaging, metrology and inspection of lithographic targets, particularly patterned structures on...doctoral thesis 2022
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Kekkonen, H.N. (author)We consider the statistical non-linear inverse problem of recovering the absorption term f > 0 in the heat equation {∂tu-12Δu+fu=0onO×(0,T)u=gon∂ O×(0,T)u(·,0)=u0onO, where O ϵ ℝd is a bounded domain, T < ∞ is a fixed time, and g, u 0 are given sufficiently smooth functions describing boundary and initial values respectively. The data...journal article 2022
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van Zwieten, G.J. (author), van Brummelen, E. Harald (author), Hanssen, R.F. (author)Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both...journal article 2022
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van der Jagt, Thomas (author)For modelling microstructures of materials the Voronoi diagram is one of the most commonly used models. In this thesis we study a generalization of Voronoi diagrams known as the Laguerre-Voronoi diagram. In particular, we consider the stereological problem of estimating the 3D cell volume distribution of such a diagram from one of its 2D planar...master thesis 2021
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Abdi, Bahareh (author)Atrial fibrillation (AF) is a common age-related cardiac arrhythmia. AF is characterized by rapid and irregular electrical activity of the heart leading to a higher risk of stroke and heart failure. During AF, the upper chambers of the heart, called atria, experience chaotic electrical wave propagation. However, despite the various mechanisms...doctoral thesis 2021
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Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable...journal article 2021
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Fuchs, P.S. (author)Electrical properties, the conductivity and permittivity of tissue, are quantities that describe the interaction of an object and electromagnetic fields. These properties influence electromagnetic fields and are influenced themselves by physiological phe- nomena such as lesions or a stroke. Therefore, they are important in identifying or...doctoral thesis 2020